Editing Universal Superposition of Orthogonal States
Jump to navigation
Jump to search
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 10: | Line 10: | ||
* '''Mixed Output Case:''' In the second case, the circuit is the same as for the pure output case. The only difference is that at the measurement step, regardless of the outcome of the measurements, we will not ignore any rounds and all the outcome states are valid superposition but they differ by a relative phase with each other (with negative or positive sign). As a result, the output of the circuit will be always a desired superposed state. In the cases which the relative phase of the superposition can be ignored, this case can be considered as a deterministic protocol. | * '''Mixed Output Case:''' In the second case, the circuit is the same as for the pure output case. The only difference is that at the measurement step, regardless of the outcome of the measurements, we will not ignore any rounds and all the outcome states are valid superposition but they differ by a relative phase with each other (with negative or positive sign). As a result, the output of the circuit will be always a desired superposed state. In the cases which the relative phase of the superposition can be ignored, this case can be considered as a deterministic protocol. | ||
== | ==Notations== | ||
*<math>\alpha</math> , <math>\beta</math>: weights of the superposition (<math>|\alpha|^2 + |\beta|^2 = 1</math>) | *<math>\alpha</math> , <math>\beta</math>: weights of the superposition (<math>|\alpha|^2 + |\beta|^2 = 1</math>) | ||
*<math>|\psi\rangle , |\psi^\perp\rangle</math>: initial states | *<math>|\psi\rangle , |\psi^\perp\rangle</math>: initial states | ||
Line 23: | Line 23: | ||
**'''mixed output case:''' In this case, $P_{succ} = 1$ and the described protocol is perfect. | **'''mixed output case:''' In this case, $P_{succ} = 1$ and the described protocol is perfect. | ||
== | ==Pseudo Code== | ||
'''<u>Stage 1</u>''' Preparation and operation</br></br> | '''<u>Stage 1</u>''' Preparation and operation</br></br> | ||
*'''Input:''' The ancillary state <math>|a\rangle = \alpha|1\rangle + \beta |0\rangle</math>, <math>|\psi\rangle</math>, <math>|\psi^\perp\rangle</math> | *'''Input:''' The ancillary state <math>|a\rangle = \alpha|1\rangle + \beta |0\rangle</math>, <math>|\psi\rangle</math>, <math>|\psi^\perp\rangle</math> | ||
Line 52: | Line 52: | ||
# [https://arxiv.org/abs/1708.04360 DKK(2017)] The above protocol | # [https://arxiv.org/abs/1708.04360 DKK(2017)] The above protocol | ||
# [https://arxiv.org/abs/1505.04955 OGHW(2016)] The first paper that talks about and proves the no-superposition theorem. Also in this paper, they present a probabilistic protocol for superposing two arbitrary (but not completely unknown) states where we know the overlaps of them with a fixed reference state. this protocol, is also restricted to a set of input states. | # [https://arxiv.org/abs/1505.04955 OGHW(2016)] The first paper that talks about and proves the no-superposition theorem. Also in this paper, they present a probabilistic protocol for superposing two arbitrary (but not completely unknown) states where we know the overlaps of them with a fixed reference state. this protocol, is also restricted to a set of input states. | ||
<div style='text-align: right;'>''*contributed by Mina Doosti''</div> | <div style='text-align: right;'>''*contributed by Mina Doosti''</div> |